I think what you want to do is called "waitlisting" an award. It can be done on awards that are just United (you can't waitlist Star Alliance carriers, for example you can't waitlist a Lufthansa flight).

The idea is that you book one flight and put yourself on the "waitlist" for the flight you would prefer to get. If in the future award inventory ever opens up on the flight you prefer, you'll be confirmed on that flight instead.

This is the term you'll want to search for, and you'll want to see how the rules stack up for waitlisting awards with United miles vs. with Continental miles (since they are still separate programs with separate rules, for now).

On United, there is a separate extra process where if there is availability for a coach award but not a business-class award, you can book the coach award, pay the business-class price, and "waitlist" for the business-class award; in that case you'll end up ranked very high on the departure-management upgrade list and are very likely to get a seat in the cabin you asked for. CO has a similar setup, described as "plan b" in the FAQ. There are some subtleties so you'll wan to be careful before you do this.

Budget at least an hour to read through forum posts and figure out the best way to do what you want, and don't hesitate to ask here!